Application of Markov Chain Stochastic Model to Lithofacies Analysis: A Case Study of Outcropping Rocks of the Lokoja Formation - Southern Bida Basin, Nigeria

Abstract

Over the years, the interpretation of the stratigraphic order or sequence of sedimentation in the Southern Bida Basin has been qualitative. More often than not, the precision of interpretation has been adjudged subjective. A more precise method used to predict the probability of the process of sedimentation, determine its cyclicity or otherwise, and ensure objective interpretation is the Markov Chain Stochastic Process. The distinct lithofacies from outcropping rocks of the Lokoja Formation, Southern Bida Basin Nigeria, were statistically analysed using the Markov Chain Stochastic Process to ascertain the degree of order. This is the first time such a model will be used in the southern region of Nigeria's Bida Basin. This made it easier to assess the basin's lithostratigraphic sequence's cyclicity. Based on the transition patterns of lithofacies, the Difference Matrix (DM) was computed, and the resultant X2 value - {Σ (DM) 2/ (ITM)} indicated that X2 = 54.27. The formula DF (N-1)2 = (N-1)2 = X was used to calculate the total of degrees of freedom (DF). Here, (X) 0 = Y and N = sum total of lithofacies in the Independent Transition Matrix (ITN) with non-zero entries (N = 7). DF = (7-1)2 = 62 = 36օ (N-1)2. When contrasted with the Chi-Square table, it was found that the value was above the X2 limiting value at a 95% confidence interval, or (X2.0.95) at 34օ degrees of freedom = 48.00 and 38օ degrees of freedom = 53.38. Therefore, the null hypothesis (Ho) was rejected, as the sedimentation process leading to the lithofacies transition pattern was considered a Markovian product with a “memory function." The precision of this result proved that the lithostratigraphic sequence is an ordered cyclic event.